交换代数

局部化（Localization）方法是交换代数中一个重要工具，通过研究一个代数簇（AlgebraicVariety）在某点或某点附近的局部性质，往往可以把握代数簇的整体特性。

Method of localization is a important tool in Commutative Algebra . The whole properties are always obtained by studying local properties of Algebraic Variety .

对于交换代数、代数几何和奇点理论，SINGULAR计算机代数系统在软件包内核以及共享库中提供了大量的算法。

For commutative algebra , algebraic geometry , and singularity theory , the SINGULAR computer algebra system provides a large variety of algorithms in the package kernel as well as shared libraries .

本文构造了AH与A~H的Morita关系，其中H是半单弱Hopf代数，A是左H-模交换代数。

It constructs a Morita context relating A # H and AH , where H is a semisimple weak Hopf algebra , A is a left H & module commutative algebra .

本文根据矩阵的Jordan标准形建立矩阵的交换代数的构造方法，在此基础上导出双线性系统的对称代数，并给出寻找一般非线性系统的对称群的一种途径。

In this paper the construction of commutative algebras for a matrix is established according to its Jordan canonical matrix . From this the symmetry algebra of a bilinear system is derived and a way of finding the symmetry group for a nonlinear system is presented .

交换代数中二次方程的求根公式

Real Coefficient Quadratic Equations Formula of Root on Real Commutative Algebra

学生需要对交换代数和基本拓扑学有一定的了解。

Students should have some familiarity with commutative algebra and basic topology .

交换代数中一个命题的简单证明

A Simple Proof of a Proposition in Commutative Algebra

有限维交换代数上导子的提升

Lifting of derivations over finite-dimensionally commutative algebras

同时，交换代数本质上是研究交换环的。

At the same time , commutative rings are studied in Commutative Algebra in nature .

量子交换代数的整体同调维数

Homological Dimension of Quantum Commutative Algebra

研究了代数闭域上三维交换代数的分类。

In this paper , we discuss the classification of3-dimensionally commutative algebras on algebraically closed field .

分式环和分式模以及与之相关的局部化方法是交换代数中一个重要工具。

The fractional ring ( module ) and the interrelated localization method are the important tools for commutative algebra .

局部上同调模在交换代数和代数几何的研究中起着重要的作用。

The theory of local cohomology modules plays an important role in the study of commutative algebra and algebraic geometry .

交换代数中最核心的概念就是素理想。

CFSTI ( Clearinghouse for Federal Scientific and Technical Information ) The central notion in commutative algebra is that of a prime ideal .

模的理论是现代数学中越来越重要的工具，它统一了许多数学结构，也是研究交换代数的基本工具。

The theory of modules is increasingly important in modern mathematics . It unifies many mathematical structures , and is the basic tools in commutative algebra .

Zn在交换AF-代数上的作用

Action of Z_n on commutative AF-algebras

交换Banach代数上线性系统的实现

Realization theory of linear systems defined over a commutative Banach algebra

复交换Banach代数中可约元的等价条件

Equivalent conditions for reducible elements of a complex commutative Banach algebra

进一步，我们刻划了交换Hilbert代数。

Moreover , some characterizations of Hilbert algebras are presented .

交换Banach代数的谱延拓性质

The spectral extension property of commutative Banach algebra

在这一章的最后，我们简要地介绍了非交换算子代数C（Dx，Dy，x，y）中的主要结论，并讨论了带有积分号的恒等式的自动证明问题。

At the end of this chapter , we introduce the main results in C and discuss the problem of verifying the identities with the integral sign .

设H是域k上的有限维余交换Hopf代数，A是H-模代数，AσH是相应的crossed积。

Throughout this paper , we work over a fixed field k. Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra . A # ~ H is the associated crossed product .

主要结果是：交换FI代数可同构嵌入一族全序交换FI代数的直积；

The main results are : Each Commutative FI algebra can be embedded into direct product of a system of linearly ordered Commutative FI algebra s ;

在有限二元树的同构类集合生成的向量空间上，利用二元树的节序列定义一个余乘法，得到了一个分次、余交换Hopf代数。

We define a coproduct on the vector space which has as basis all finite binary trees by using their spine sequences , and construct a cocommutative graded connected Hopf algebra .

设G为半单矩阵群，g为其Lie代数，T为g的极大交换子代数，T~⊥为T关于g的Killing型（，）的正交补，a，b∈T为固定正则元。

Let G be semisimple matrix group with Lie algebra g , T a fixed maximal abelian subalgebra of g , T the orthogonal complement of T with respect to the Killing form < , > of g , and a , b 6 T a fixed regular elements .

本文讨论了交换Banach代数A的乘子代数（A）的若干性质，并且得到了如下的结论：如果A是一个忠实交换的~代数，那么M（A）也是一个交换的~代数。

In this paper we discuss some properties of M ( A ), the multiplier algebra of a commutative BANACH algebra A , and obtain the following result : If A is a faithful commutative-algebra , then so is M ( A ) .

非交换Rota-Baxter代数的若干应用

Some Applications of Noncommutative Rota-Baxter Algebras

本文在对Novikov代数的研究中，建立了Novikov代数与其他代数如李代数、交换结合代数的关系，并通过此关系进一步建立Novikov代数与常见具体函数的同构，用常见函数对其进行实现。

In this thesis , we will establish the relation between Novikov algebras and other alge-bras , such as Lie algebra abelian algebra by the study of the Novikov algebra .

本文引入离散型BCK代数概念，并探讨它与原子生成的BCK代数、正关联BCK代数、交换BCK代数之间的关系及其自身的一些代数性质。

In this paper , we shall introduce the concept of discrete BCK algebra , and discuss its relation with BCK-algebra generated by atoms , positive implicative BCK-algebra , commutative BCK algebra and its self algebraic properties .

Arad和Blau在1991年从有限群的不可约特征标和共轭类的积的分解中抽象出表代数的概念，它是一类满足特定条件的定义在复数域上的有限维交换结合代数。

Arad and Blau abstracted the concept of table algebras , which are a class of finite dimensional , associative and commutative algebras over the complex numbers with certain specified properties , from the decompositions of products of either irreducible characters or conjugacy classes of finite groups .